Fracture dependence on modes of loading - Modes I, II and III
In some engineering failures, the detail of collapse frequently is related to cracking, through overload, stress corrosion cracking (SCC) or fatigue, for example. The mode of fracture can reveal a great deal about the stress state at the time of loading and fracture, and there are characteristic features that can be recognised which assist in the determination of how the cracking developed and failure took place. This Technical Tip discusses these and their characteristics, and how useful this can be to the failure analysis investigator.
It is convenient to regard crack development in metals as occurring in one of three modes, (as well as in combinations of these). Pure tensile loading, for example at right angles to the crack plane of a notched plate, is regarded as Mode I (opening mode), with separation of the crack plane surfaces away from each other. If the same type of starter crack or notch was to be loaded in pure ‘in plane’ shear, cracking could proceed parallel to the crack plane, due to the direct shear loading. This so called ‘sliding loading’, is characterised as Mode II cracking. The third mode of loading and cracking that can occur with the same starter crack notch geometry in a plate, is ‘out of plane’ shear, typified by the tearing of a sheet of paper, say. This type of loading and its consequent fracture surface is known as Mode III cracking, and is typical of torsional loading situations.
When one measures the fracture toughness of a metal, one invariably refers to the Mode I ‘opening’ load case, as is typical for a beam in bending or the opening of a crack in a compact tension specimen. However, measurement of the other modes (II and III) is possible through specialised specimen configurations, but their values (Mode II and III toughness) are typically higher than Mode I toughness. However, it is worth bearing in mind that the cracking mode which initiates at the lowest stress is Mode I, which is also the most commonly encountered. Cracks which may develop at a very small size through fretting or shear for example, and located at 45 degrees to the principal stress, will turn around in a stress field to grow (in fatigue) perpendicular to the principal applied stress field direction, as a typical Mode I loaded crack.
The fracture surfaces associated with each of the three Modes of cracking are also unique and distinct. Mode I cracking, in fatigue for example, is perpendicular to the applied stress, and is typically planar and flat, with typical so called ‘clamshell’ markings (in the case of fatigue cracking). Mode II loading is typified by shear which is characterised by surface cracking, and in certain cases, complementary shear which occurs at right angles to the original, often longitudinal, cracks. In torsional applications, this can lead to fracture surfaces appearing in both the longitudinal directions (on the outside cylindrical surface) as well as in complementary shear at right angles to this. As cracks develop and grow, through fatigue for example in towards the core of a round shaft, the fracture surfaces appear as a ratcheted surface, not unlike a ‘factory roof’. This type of fracture surface is frequently encountered in torsional failure cases. Thus in torsional failures the crack path is tortuous and ratchetted, and certainly not flat as is the case of a fine Mode I fatigue crack.
The fracture surfaces referred to above allude to a more macroscopic surface appearance, but if one was to look at the surface more carefully, the microscopic fracture appearance is also helpful in revealing cracking directions and loading features. A pure tensile test would typically exhibit ductile micro-void coalescence (MVC), which is extended in pure Mode I loading to appear as Capital C shaped crescent moon shapes, with the arms (of the moon) pointing to the already opened side of the crack. In Mode II, these crescent moon C shapes on opposite fracture surfaces point back to each other since they were formed in shear, so that the C shapes of one surface point to the left (say) while those of the opposite surface point to the right. A similar effect, of the C arms pointing towards each other, would also be apparent in the tearing mode or torsion, but at a reduced scale.
Together with macro fracture surface features, these micro-void features can be used to identify the mode of loading and of crack development and are often useful in understanding the fundamental mode of failure and particularly initiation which may occur due to Mode II or Mode III.
Published in Technical Tips by Origen Engineering Solutions on 1 August 2018